1.
If you say that something duly happened or was done, you mean that it was expected to happen or was requested, and it did happen or it was done.
Westcott appealed to Waite for an apology, which he duly received.
ADV: ADV before v
2.
If something is duly done, it is done in the correct way. (FORMAL)
...the duly elected president of the country.
ADV: ADV before v